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From: Derakon <derakon@gm...>  20110609 20:24:36

I have a program that displays 3D arrays of pixel data that have been transformed (by XYZ translation, rotation about the Z axis, and uniform scaling in X and Y  so five parameters). When possible (i.e. Z offset is 0) I use OpenGL to show the transformation since this is fast. however, when there is a Z transform, I manually construct a transformation matrix with Numpy, invert it, and use it to map display coordinates into the data to determine what needs to be shown. That is, I have a bunch of XY coordinates, one for each pixel I want to display (e.g. from [0, 0] to [512, 512]), I reversetransform them, this gives me a location in the dataset, and that gets me the value to display. There's a problem here: the two approaches generate different results. For example, here's my flat 512x512 test image (disregarding the Z dimension), untransformed (the grey lines are for reference and are not part of the image): http://derakon.dyndns.org/~chriswei/temp2/1.png Here's the image rotated 45° and translated 20 pixels in X, in OpenGL: http://derakon.dyndns.org/~chriswei/temp2/2.png (Ignore the grey triangles; they're just a display artifact) And here's that same image with the transformation applied via Numpy: http://derakon.dyndns.org/~chriswei/temp2/3.png The last example is the behavior I actually want  rotation should be about the center of the image, and applied before translation occurs. However that's not what I'm getting from my OpenGL transformation code. I've put up a paste comparing the two approaches and what I get when I print their transformation matrices, here: http://pastebin.com/j31iLGbT Any ideas what I'm doing wrong here? I note that if I swap the order of the glRotated and glTranslated calls, then I get OpenGL matrices that look more like what I'm getting from Numpy, but of course the rotation is no longer about the center of the image, so the results are even more off. Chris 
From: Ian Mallett <geometrian@gm...>  20110609 20:48:42
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On Thu, Jun 9, 2011 at 1:24 PM, Derakon <derakon@...> wrote: > I have a program that displays 3D arrays of pixel data that have been > transformed (by XYZ translation, rotation about the Z axis, and > uniform scaling in X and Y  so five parameters). When possible (i.e. > Z offset is 0) I use OpenGL to show the transformation since this is > fast. however, when there is a Z transform, I manually construct a > transformation matrix with Numpy, invert it, and use it to map display > coordinates into the data to determine what needs to be shown. That > is, I have a bunch of XY coordinates, one for each pixel I want to > display (e.g. from [0, 0] to [512, 512]), I reversetransform them, > this gives me a location in the dataset, and that gets me the value to > display. > > There's a problem here: the two approaches generate different results. > For example, here's my flat 512x512 test image (disregarding the Z > dimension), untransformed (the grey lines are for reference and are > not part of the image): > http://derakon.dyndns.org/~chriswei/temp2/1.png > > Here's the image rotated 45° and translated 20 pixels in X, in OpenGL: > http://derakon.dyndns.org/~chriswei/temp2/2.png > > (Ignore the grey triangles; they're just a display artifact) > > And here's that same image with the transformation applied via Numpy: > http://derakon.dyndns.org/~chriswei/temp2/3.png > > The last example is the behavior I actually want  rotation should be > about the center of the image, and applied before translation occurs. > However that's not what I'm getting from my OpenGL transformation > code. I've put up a paste comparing the two approaches and what I get > when I print their transformation matrices, here: > http://pastebin.com/j31iLGbT > > Any ideas what I'm doing wrong here? I note that if I swap the order > of the glRotated and glTranslated calls, then I get OpenGL matrices > that look more like what I'm getting from Numpy, but of course the > rotation is no longer about the center of the image, so the results > are even more off. > Switch lines 11 and 12. 
From: Derakon <derakon@gm...>  20110609 20:50:17

Never mind, problem solved! The issue was that my second translation was getting rotated, which was undesirable. In fact what I wanted was to do this: glTranslated(dx + cx, dy + cy) glRotated(angle, 0, 0, 1) glTranslated(cx, cy, 0) I'd tried the line swap that Ian suggested earlier, and it didn't work (as noted in the last paragraph of my previous message), but this appears to get me what I want. Chris On Thu, Jun 9, 2011 at 1:24 PM, Derakon <derakon@...> wrote: > I have a program that displays 3D arrays of pixel data that have been > transformed (by XYZ translation, rotation about the Z axis, and > uniform scaling in X and Y  so five parameters). When possible (i.e. > Z offset is 0) I use OpenGL to show the transformation since this is > fast. however, when there is a Z transform, I manually construct a > transformation matrix with Numpy, invert it, and use it to map display > coordinates into the data to determine what needs to be shown. That > is, I have a bunch of XY coordinates, one for each pixel I want to > display (e.g. from [0, 0] to [512, 512]), I reversetransform them, > this gives me a location in the dataset, and that gets me the value to > display. > > There's a problem here: the two approaches generate different results. > For example, here's my flat 512x512 test image (disregarding the Z > dimension), untransformed (the grey lines are for reference and are > not part of the image): > http://derakon.dyndns.org/~chriswei/temp2/1.png > > Here's the image rotated 45° and translated 20 pixels in X, in OpenGL: > http://derakon.dyndns.org/~chriswei/temp2/2.png > > (Ignore the grey triangles; they're just a display artifact) > > And here's that same image with the transformation applied via Numpy: > http://derakon.dyndns.org/~chriswei/temp2/3.png > > The last example is the behavior I actually want  rotation should be > about the center of the image, and applied before translation occurs. > However that's not what I'm getting from my OpenGL transformation > code. I've put up a paste comparing the two approaches and what I get > when I print their transformation matrices, here: > http://pastebin.com/j31iLGbT > > Any ideas what I'm doing wrong here? I note that if I swap the order > of the glRotated and glTranslated calls, then I get OpenGL matrices > that look more like what I'm getting from Numpy, but of course the > rotation is no longer about the center of the image, so the results > are even more off. > > Chris > 
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